Based on the R2 value, it is obvious, Langmuir is not the right model to explain your adsorption equilibrium data. Even if both fits equally well, you an decide based on the shape and the number of points in the isotherm. If you worked out only the adsorption at lower concentration then it is obvious both Langmuir and Freundlich fits the data. If you have a complete isotherm from lower to higher pressures, then you will have different scenario.

Also it is up to you to decide as these isotherms at the end of the day are used to design a batch adsorber, thus any of these isotherms can used top design the adsorption system.

Qm in Langmuit and K value in Freundlich are not comparable as they have different units. Freundlich is a special case of Langmuir at lower pressures when n = 1. So the final answer is NO - you cannot compare them. 

Mr kumar thank you for the answer. I Know that Freundlich is a right model to describe my system. However my question is could I use the Qm (of Langmuir model) and compare this value to other Qm values event my system is not well fitted to the Langmuir Model (only an R2 of about 0.82).

It is tricky. For example you can compare the Qm value of Langmuir with Qm of Sips isotherm or Qm of Toth isotherm. But the meaning of Qm will be different. 

In the case of Langmuir Qm corresponds to the number of sites with a binding energy equivalent to kL.

In the case of Sips or Toth isotherm or other isotherms like Redlich-Peterson, Qm corresponds to one of the many sites that are avaialble on the adsorbent surface..the Qm probably you get will correspond to adsorption site with the weakest binding energy (as the adsorption site with weakest binding energy will give access to the adsorbate molecule only at higher pressure).

If you are using Sips or Toth or Redlich Peterson you can use some expressions to interpret the results.

Check this please: A continuous site energy distribution function from Redlich–Peterson isotherm for adsorption on heterogeneous surfaces

hope this helps

 if you want you can send me the data, i will try to calculate the binding energy distribution for u..

THANKS AGAIN.

I found very good informations in your answer. 

Qm (Langmuir model) of my adsorbents could be then compared to Qm ( Langmuir model) of other adsorbents ?

My aim is not to compare the Qm of differents models Lngmuir, sips and soon) but the Qm (langmuir model) of differents adsorbents.

Do you think is it possible in my case ? 

Thanks in advance.

why you need compare the Qm? Qm in Langmuir means the maximum capacity that saturates your adsorbents, so, you do not need to fit langmuir ... If you can see the saturation in your q-C data, you can consider your saturation and compare with other people Langmuir Qm which means the same as  yours. 

Best Regards,

Mohammad

Ok !! Thanks Mr Mohammad.

In fact I want to compare the maximum capacity of my materials with similar materials (values found in the literature).

Sincerely

Achraf 

yes, you can compare as many adsorbents u want based on QM...you can even compare Qm from literature with yours..make it sure.,you have a complete isotherm and also make it sure with the literature as well. some just predict qm based on isotherm obtained at very low pressure or concentration,,,,such values might be over estimated...long time before i studied something about this issue

EQUILIBRIUM DATA, ISOTHERM PARAMETERS AND PROCESS DESIGN FOR PARTIAL AND COMPLETE ISOTHERM OF METHYLENE BLUE ONTO ACTIVATED CARBON

you can have a look if you have time.

Perfect. Very useful paper.

Many thanks for answers. 

No probs. good luck with your research.